05 Jun Question Vancouver School of Economics UBC Assignment #2 Due date: June 19, 2015
Question
Vancouver School of Economics
UBC
Assignment #2
Due date: June 19, 2015
Question # 1
Consider a two-period mine (periods 0 and 1) industry that is owned by a monopoly
firm. Let interest rates, demand, extraction costs, and initial stock be give by: r = 5%,
P(Qt) = 100 – Qt/2, MC = $50/barrel, S0 = 150 barrel. (4+5+6 points)
(a) Set up the maximization problem and Lagrangian for this monopoly firm.
(b) Solve the above maximization problem using Lagrangian multiplier method.
Calculate the scarcity rent. Test if you get negative rent.
(c) If scarcity rent is negative, then that means scarcity rent is zero. Use the correct
method to solve this maximization problem.
Question #2
The market for power supply in Lower Mainland, BC consists of 4 large and 10 smaller
firms. The large firms each has a cost function as follows: CL = 0.5qL
2. The small firms
each has a cost function as follows: CS = 5qs
2. The market demand curve is: P = 1200 –
Q. (5+10+5 points)
(a) Calculate the equilibrium price and quantity that would prevail if all firms act as
competitive price-taking firms?
(b) What are the equilibrium price and total quantity when the 4 large firms act as a
cartel, and the remaining smaller firms take the price determined by the cartel as
given? Draw a diagram to illustrate your results.
(c) If all of these 14 firms merge together and act as a single firm, what would be the
resulting equilibrium price and quantity?
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